Projective Geometric Algebra in Plane and Its Implementation in the Library Ganja.js

Abstract: Geometric algebra is currently considered as a universal mathematical apparatus of computer graphics. Active research, both academic and applied, is being conducted in this area. Due to the applied nature of the research, many results are immediately implemented in the form of computer program code and libraries. One of such libraries is Ganja.js The aim of this paper is to review some capabilities of Ganja.js using the example of projective geometric algebra in its dual version. The paper uses the apparatus of linear algebra, elements of projective geometry, and geometric algebra (Clifford and Grassmann algebras). The software tools used are those of JavaScript. Ganja.js implements a mathematical syntax that allows you to define various Clifford algebras, manipulate their elements using algebraic operations, and visualize algebra elements as geometric objects. The created visualizations can be interactive and animated. Even though JavaScript is a completely unusual language for academic mathematical research, Ganja.js can be a useful tool for computation, visualization, and research in geometric algebra. © Pleiades Publishing, Ltd. 2025.